{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T08:06:11Z","timestamp":1761897971665,"version":"3.37.3"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2024,3,11]],"date-time":"2024-03-11T00:00:00Z","timestamp":1710115200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,3,11]],"date-time":"2024-03-11T00:00:00Z","timestamp":1710115200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62171388","61871461","61571374"],"award-info":[{"award-number":["62171388","61871461","61571374"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1007\/s00034-024-02637-x","type":"journal-article","created":{"date-parts":[[2024,3,11]],"date-time":"2024-03-11T12:02:17Z","timestamp":1710158537000},"page":"3888-3908","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Robust Variable Step Size Widely Linear Complex-Valued Least Mean M-estimate Adaptive Algorithm: Derivation and Performance Analysis"],"prefix":"10.1007","volume":"43","author":[{"given":"Shaohui","family":"Lv","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4756-771X","authenticated-orcid":false,"given":"Haiquan","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenjing","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,3,11]]},"reference":[{"key":"2637_CR1","doi-asserted-by":"publisher","first-page":"290","DOI":"10.1016\/j.sigpro.2014.11.018","volume":"109","author":"R Arablouei","year":"2015","unstructured":"R. Arablouei, K. Do\u011fan\u00e7ay, S. Werner, Adaptive frequency estimation of three-phase power systems. Signal Process. 109, 290\u2013300 (2015)","journal-title":"Signal Process."},{"issue":"7","key":"2637_CR2","doi-asserted-by":"publisher","first-page":"1689","DOI":"10.1109\/TSP.2012.2236831","volume":"61","author":"ZA Bhotto","year":"2013","unstructured":"Z.A. Bhotto, A. Antoniou, A family of shrinkage adaptive-filtering algorithms. IEEE Trans. Signal Process. 61(7), 1689\u20131697 (2013)","journal-title":"IEEE Trans. Signal Process."},{"key":"2637_CR3","doi-asserted-by":"publisher","first-page":"994","DOI":"10.1007\/s00034-023-02492-2","volume":"43","author":"Z Cao","year":"2024","unstructured":"Z. Cao, H. Zhao, Y. Liu, Y. Chen, Complex total least mean M-estimate adaptive algorithm for noisy input and impulsive noise. Circuits Syst. Signal Process. 43, 994\u20131006 (2024)","journal-title":"Circuits Syst. Signal Process."},{"key":"2637_CR4","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1016\/j.sigpro.2013.09.017","volume":"97","author":"P Chevalier","year":"2014","unstructured":"P. Chevalier, J.-P. Delmas, A. Oukaci, Properties, performance and practical interest of the widely linear MMSE beamformer for nonrectilinear signals. Signal Process. 97, 269\u2013281 (2014)","journal-title":"Signal Process."},{"issue":"3","key":"2637_CR5","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1109\/6046.784467","volume":"1","author":"PG Georgiou","year":"1999","unstructured":"P.G. Georgiou, P. Tsakalides, C. Kyriakakis, Alpha-stable modeling of noise and robust time-delay estimation in the presence of impulsive noise. IEEE Trans. Multimed. 1(3), 291\u2013301 (1999)","journal-title":"IEEE Trans. Multimed."},{"issue":"1","key":"2637_CR6","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1109\/LSP.2016.2634534","volume":"24","author":"JPF Guimaraes","year":"2017","unstructured":"J.P.F. Guimaraes, A.I.R. Fontes, J.B.A. Rego, A.M. de Martins, J.C. Principe, Complex correntropy: probabilistic interpretation and application to complex-valued data. IEEE Signal Process. Lett. 24(1), 42\u201345 (2017)","journal-title":"IEEE Signal Process. Lett."},{"key":"2637_CR7","doi-asserted-by":"publisher","DOI":"10.1016\/j.dsp.2021.103087","volume":"115","author":"G Huang","year":"2021","unstructured":"G. Huang, M. Shen, T. Zhang, F. He, S. Wang, Complex multi-kernel random Fourier adaptive algorithms under the complex kernel risk-sensitive p-power loss. Digit. Signal Process. 115, 103087 (2021)","journal-title":"Digit. Signal Process."},{"key":"2637_CR8","unstructured":"S. Javidi, M. Pedzisz, S. L. Goh, D. Mandic, The augmented complex least mean square algorithm with application to adaptive prediction problems, in 1st IARP Workshop Cogn. Inf. Process. (2008), pp. 54\u201357"},{"key":"2637_CR9","doi-asserted-by":"publisher","DOI":"10.1016\/j.dsp.2021.102968","volume":"111","author":"EV Kuhn","year":"2021","unstructured":"E.V. Kuhn, C.A. Pitz, M.V. Matsuo, K.J. Bakri, R. Seara, J. Benesty, A Kronecker product CLMS algorithm for adaptive beamforming. Digit. Signal Process. 111, 102968 (2021)","journal-title":"Digit. Signal Process."},{"issue":"10","key":"2637_CR10","doi-asserted-by":"publisher","first-page":"5785","DOI":"10.1007\/s00034-022-02053-z","volume":"41","author":"L Li","year":"2022","unstructured":"L. Li, Y. Pu, Widely linear complex-valued least mean m-estimate algorithms: design and performance analysis. Circuits Syst. Signal Process. 41(10), 5785\u20135806 (2022)","journal-title":"Circuits Syst. Signal Process."},{"issue":"12","key":"2637_CR11","doi-asserted-by":"publisher","first-page":"7645","DOI":"10.1016\/j.jfranklin.2023.06.038","volume":"360","author":"S Lv","year":"2023","unstructured":"S. Lv, H. Zhao, W. Xu, Robust augmented complex-valued normalized M-estimate subband adaptive filtering algorithm against colored non-circular inputs and impulsive noise. J. Frankl. Inst. 360(12), 7645\u20137675 (2023)","journal-title":"J. Frankl. Inst."},{"key":"2637_CR12","doi-asserted-by":"publisher","first-page":"3623","DOI":"10.1109\/TSP.2023.3311880","volume":"71","author":"S Lv","year":"2023","unstructured":"S. Lv, H. Zhao, W. Xu, Robust widely linear affine projection M-estimate adaptive algorithm: performance analysis and application. IEEE Trans. Signal Process. 71, 3623\u20133636 (2023)","journal-title":"IEEE Trans. Signal Process."},{"issue":"1","key":"2637_CR13","first-page":"234","volume":"69","author":"S Lv","year":"2022","unstructured":"S. Lv, H. Zhao, L. Zhou, Robust proportionate normalized least mean M-estimate algorithm for block-sparse system identification. IEEE Trans. Circuits Syst. II Express Br. 69(1), 234\u2013238 (2022)","journal-title":"IEEE Trans. Circuits Syst. II Express Br."},{"issue":"1","key":"2637_CR14","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1016\/j.renene.2008.03.022","volume":"34","author":"DP Mandic","year":"2009","unstructured":"D.P. Mandic, S. Javidi, S.L. Goh, A. Kuh, K. Aihara, Complex-valued prediction of wind profile using augmented complex statistics. Renew. Energy 34(1), 196\u2013201 (2009)","journal-title":"Renew. Energy"},{"issue":"2","key":"2637_CR15","doi-asserted-by":"publisher","first-page":"438","DOI":"10.1109\/TSP.2017.2768024","volume":"66","author":"EC Menguc","year":"2018","unstructured":"E.C. Menguc, N. Acir, An augmented complex-valued least-mean kurtosis algorithm for the filtering of noncircular signals. IEEE Trans. Signal Process. 66(2), 438\u2013448 (2018)","journal-title":"IEEE Trans. Signal Process."},{"issue":"2","key":"2637_CR16","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1109\/TIT.1958.1057444","volume":"4","author":"R Price","year":"1958","unstructured":"R. Price, A useful theorem for nonlinear devices having Gaussian inputs. IEEE Trans. Inf. Theory 4(2), 69\u201372 (1958)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2637_CR17","doi-asserted-by":"publisher","first-page":"19113","DOI":"10.1109\/ACCESS.2018.2821141","volume":"6","author":"G Qian","year":"2018","unstructured":"G. Qian, S. Wang, Generalized complex correntropy: application to adaptive filtering of complex data. IEEE Access 6, 19113\u201319120 (2018)","journal-title":"IEEE Access"},{"key":"2637_CR18","volume-title":"Fundamentals of Adaptive Filtering","author":"AH Sayed","year":"2003","unstructured":"A.H. Sayed, Fundamentals of Adaptive Filtering (IEEE Press Wiley-Interscience, New York, 2003)"},{"issue":"1","key":"2637_CR19","doi-asserted-by":"publisher","first-page":"133","DOI":"10.2307\/2982847","volume":"152","author":"AH Seheult","year":"1989","unstructured":"A.H. Seheult, P.J. Green, P.J. Rousseeuw, A.M. Leroy, Robust Regression and Outlier Detection. J. R. Stat. Soc. Ser. A Stat. Soc. 152(1), 133 (1989)","journal-title":"J. R. Stat. Soc. Ser. A Stat. Soc."},{"key":"2637_CR20","doi-asserted-by":"publisher","first-page":"5940","DOI":"10.1109\/TSP.2020.3029884","volume":"68","author":"L Shi","year":"2020","unstructured":"L. Shi, H. Zhao, Y. Zakharov, B. Chen, Y. Yang, Variable step-size widely linear complex-valued affine projection algorithm and performance analysis. IEEE Trans. Signal Process. 68, 5940\u20135953 (2020)","journal-title":"IEEE Trans. Signal Process."},{"key":"2637_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.sigpro.2019.06.029","volume":"165","author":"L Shi","year":"2019","unstructured":"L. Shi, H. Zhao, X. Zeng, Y. Yu, Variable step-size widely linear complex-valued NLMS algorithm and its performance analysis. Signal Process. 165, 1\u20136 (2019)","journal-title":"Signal Process."},{"issue":"2","key":"2637_CR22","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1016\/j.sigpro.2012.08.017","volume":"93","author":"C Stanciu","year":"2013","unstructured":"C. Stanciu, J. Benesty, C. Paleologu, T. G\u00e4nsler, S. Ciochin\u0103, A widely linear model for stereophonic acoustic echo cancellation. Signal Process. 93(2), 511\u2013516 (2013)","journal-title":"Signal Process."},{"key":"2637_CR23","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2021.108433","volume":"194","author":"W Xu","year":"2022","unstructured":"W. Xu, H. Zhao, Robust constrained recursive least M-estimate adaptive filtering algorithm. Signal Process. 194, 108433 (2022)","journal-title":"Signal Process."},{"key":"2637_CR24","doi-asserted-by":"publisher","first-page":"2199","DOI":"10.1109\/TSP.2020.2983905","volume":"68","author":"Y Yu","year":"2020","unstructured":"Y. Yu, H. He, T. Yang, X. Wang, R.C. de Lamare, Diffusion normalized least mean m-estimate algorithms: design and performance analysis. IEEE Trans. Signal Process. 68, 2199\u20132214 (2020)","journal-title":"IEEE Trans. Signal Process."},{"issue":"1","key":"2637_CR25","first-page":"91","volume":"64","author":"S Zhang","year":"2017","unstructured":"S. Zhang, J. Zhang, H. Han, Robust shrinkage normalized sign algorithm in an impulsive noise environment. IEEE Trans. Circuits Syst. II Express Br. 64(1), 91\u201395 (2017)","journal-title":"IEEE Trans. Circuits Syst. II Express Br."},{"issue":"13","key":"2637_CR26","doi-asserted-by":"publisher","first-page":"3592","DOI":"10.1109\/TSP.2019.2919412","volume":"67","author":"S Zhang","year":"2019","unstructured":"S. Zhang, J. Zhang, W. Zheng, H.C. So, Widely linear complex-valued estimated-input LMS algorithm for bias-compensated adaptive filtering with noisy measurements. IEEE Trans. Signal Process. 67(13), 3592\u20133605 (2019)","journal-title":"IEEE Trans. Signal Process."},{"key":"2637_CR27","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1016\/j.sigpro.2017.06.007","volume":"141","author":"S Zhang","year":"2017","unstructured":"S. Zhang, W. Zheng, J. Zhang, A new combined-step-size normalized least mean square algorithm for cyclostationary inputs. Signal Process. 141, 261\u2013272 (2017)","journal-title":"Signal Process."},{"key":"2637_CR28","doi-asserted-by":"crossref","unstructured":"H. Zhao, G. Wang, F. Zhao, D. Liu, P. Song, Recursive General Mixed Norm Algorithm for Censored Regression: Performance Analysis and Channel Equalization Application. IEEE Trans. Syst. Man Cybern, Syst. 54(2), 752\u2013763 (2024)","DOI":"10.1109\/TSMC.2023.3321115"}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-024-02637-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00034-024-02637-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-024-02637-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,30]],"date-time":"2024-05-30T15:08:33Z","timestamp":1717081713000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00034-024-02637-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,11]]},"references-count":28,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["2637"],"URL":"https:\/\/doi.org\/10.1007\/s00034-024-02637-x","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"type":"print","value":"0278-081X"},{"type":"electronic","value":"1531-5878"}],"subject":[],"published":{"date-parts":[[2024,3,11]]},"assertion":[{"value":"8 November 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 February 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 February 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 March 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}}]}}